Nambu-Covariant Many-Body Theory I: Perturbative Approximations

Abstract

Symmetry-breaking considerations play an important role in allowing reliable and accurate predictions of complex systems in quantum many-body simulations. The general theory of perturbations in symmetry-breaking phases is nonetheless intrinsically more involved than in the unbroken phase due to non-vanishing anomalous Green's functions or anomalous quasiparticle interactions. In the present paper, we develop a formulation of many-body theory at non-zero temperature which is explicitly covariant with respect to a group containing Bogoliubov transformations. Based on the concept of Nambu tensors, we derive a factorisation of standard Feynman diagrams that is valid for a general Hamiltonian. The resulting factorised amplitudes are indexed over the set of un-oriented Feynman diagrams with fully antisymmetric vertices. We argue that, within this framework, the design of symmetry-breaking many-body approximations is simplified.

Gorkov algebraic diagrammatic construction formalism at third order

“…However, let us remind that relations (29) naturally stem out from Nambu covariant theory of Ref. [40]. In this case both the normal and anomalous contributions are embedded in a single propagator such that the C and D couplings are part of a unique coupling matrix.…”

“…More importantly, the combined use of Nambu indices and an appropriate dual basis can be extended into a generalised Nambu-covariant formalism as discussed in Refs. [40,41]. In Nambu-covariant Green's function theory, all normal and anomalous propagators appear as specific elements of a unique propagator carrying the common features in their spectral representations.…”

“…This choice differs from our initial Gorkov work of Ref [25]. but maintains a continuity of notation with our other SCGF developments[16,23,[34][35][36][37][38][39][40][41]…”

Many-body approximations to the superfluid gap and critical temperature in pure neutron matter

“…( 6) to obtain an effective two-body force, W . Carefully considering the normal ordering of each contribution, one finds that in the calculation of the single-particle mean-field, Σ, one needs to employ the sum [34,53,54]. We compute the Hartree-Fock self-energy numerically with partial waves up to J = 10.…”

“…Recently, we have formulated a new theoretical framework that addresses this issue and facilitates the systematic exploration of many-body effects in superfluid systems at finite temperature [53,54]. This framework develops a diagrammatic expansion that can potentially provide systematical predictions for many-body scheme uncertainties.…”